Independent solution

How to solve this Loan Amortization question

Setup

Setup

The missed block and enlarged block have equal length, so pair each missed payment with the payment six months later that replaces it.

im=0.30/12=0.025i_m=0.30/12=0.025

Model

Model

An enlarged payment contains the regularly scheduled 500 plus the earlier missed 500 accumulated for six months.

X=500+500(1.025)6X=500+500(1.025)^6

Compute

Compute

At 2.5% per month, this paired replacement amount is 1,079.8466.

X=1079.8466X=1079.8466

Answer

Answer

The increased payment rounds to 1,080, which is choice C.

X≈1080(C)\boxed{X\approx1080\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

Check END/BGN, period, sign, TVM, and cash-flow setup

  1. 2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 6 N; 2.5 I/Y; 500 +/- PV; 0 PMT; CPT FVFV = 579.85; enlarged payment = 1079.85END mode; I/Y is the monthly effective rate. Add the current regular payment of 500.